Real Positive Semidefinite Matrix Cone
Why
The set of positive semidefinite matrices turns
out to be a cone in the vector space of $n
\times n$ matrices.
Main result
$\mathbfsf{S} _+^d$ is a convex, pointed, closed
cone with interior $\mathbfsf{S} _{++}^d$ relative
to $\mathbfsf{S} ^d$.
The cone of positive definite matrices is open.